The ambient environments in which seismic surveys are conducted contain noise that needs to be attenuated or removed from the seismic data. Irregular sampling and spatial aliasing of seismic data pose a challenge to noise attenuation. High-resolution Radon transform (or sparse Radon inversion) is effective in handling irregularly sampled and spatially aliased seismic data. In particular, the Tau-p, (τ,p), transform has been used as a powerful seismic data processing tool for many years. For example, slant-stack has been used for directional decomposition of seismic signals, and an anti-leakage Tau-p transform (ALTP), which is analogous to the anti-leakage Fourier transform (ALFT), iteratively extracts the slowness of the most dominant energy until the remainder is smaller than a predefined threshold or the maximum number of iterations is reached. This method has been modified to apply a semblance weighting to the energy of the Tau-p model and then uses it as a criterion for event selection, honoring events with better coherence.
The linear Tau-p transform was proposed to make the Tau-p transform theoretically invertible. However, in practice, discrete spatial sampling and limited spatial aperture of seismic data still rendered this method non-invertible. The linear Radon transform was then proposed to make the Tau-p transform invertible using the power of least squares fitting of the input data with a Tau-p model. This method has been modified with semblance weighting. Linear Radon transform methods need to be applied iteratively and, therefore, are very expensive. Also, these methods suffer from energy leakage among different slowness values; thus, the resolution is often low.
To mitigate energy leakage among different slowness values, which causes smearing and damage to events, a high-resolution Radon transform (or sparse Radon inversion) has been proposed that tries to fit the input data with a spiky (sparse) Tau-p model. This method handles aliasing and resolution in a non-iterative way. Thus, it is not only more accurate with higher resolution, but also more efficient.